A132057 A convolution triangle of numbers obtained from A034904.

1, 28, 1, 980, 56, 1, 37730, 2744, 84, 1, 1531838, 130340, 5292, 112, 1, 64337196, 6136956, 299782, 8624, 140, 1, 2766499428, 288408120, 16120314, 568008, 12740, 168, 1, 121034349975, 13561837212, 841627332, 34401528, 956970, 17640, 196, 1

Offset: 1

Author

Wolfdieter Lang Sep 14 2007

Keywords

• nonn
• easy
• tabl

Comments

a(n,1) = A034904(n). a(n,m)=: s2(8; n,m), a member of a sequence of unsigned triangles including s2(2; n,m)=A007318(n-1,m-1) (Pascal's triangle). s2(3;n,m)= A035324(n,m), s2(4; n,m)= A035529(n,m), s2(5; n,m)= A048882(n,m), s2(6; n,m)= A049375; s2(7; n,m)=A092083.

Examples

			{1}; {28,1}; {980,56,1}; (37730,2744,84,1);...
		

Links

• W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
• W. Lang, First 10 rows.

Crossrefs

Cf. A132058 (row sums), A132059 (negative of alternating row sums).

Programs

Mathematica

a[n_, m_] := a[n, m] = 7*(7*(n-1) + m)*a[n-1, m]/n + m*a[n-1, m-1]/n;
a[n_, m_] /; n < m = 0; a[_, 0] = 0; a[1, 1] = 1;
Flatten[Table[a[n, m], {n, 1, 8}, {m, 1, n}]][[1 ;; 36]]
(* Jean-François Alcover, Jun 17 2011 *)

Formula

a(n, m) = 7*(7*(n-1)+m)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n

G.f. for m-th column: ((-1+(1-49*x)^(-1/7))/7)^m.

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